Effect of vibronic relaxation in fluorescence resonance energy transfer: An exact analytical solution

TL;DR

This paper presents an exact analytical solution for FRET that incorporates vibronic relaxation effects, revealing that neglecting these relaxations can lead to overestimating donor-acceptor distances.

Contribution

It introduces a Green's function based formalism to accurately model vibronic relaxation in FRET, extending beyond the traditional Förster theory.

Findings

Vibronic relaxation significantly affects FRET rates.

Neglecting vibronic effects overestimates donor-acceptor distance.

The model provides a more accurate description of energy transfer dynamics.

Abstract

Fluorescence resonance energy transfer (FRET) is widely used as a 'spectroscopic ruler' to measure fluctuations in macromolecules because of the strong dependence of the rate on the separation (R) between the donor (D) and acceptor (A). However, the well-known Forster rate expression that predicts an $R^{-6}$ dependence, is limited by several approximations. Notable among them is the neglect of the vibronic relaxation in the reactant (donor) and product (acceptor) manifolds. Vibronic relaxation can play an important role when the energy transfer rate is faster than the vibronic relaxation rate. Under such conditions, donor to acceptor energy transfer can occur from the excited vibronic states. This phenomenon is not captured by the usual formulation based on the overlap of donor emission and acceptor absorption spectra. Here, we attempt to eliminate this lacuna, by allowing relaxation in the vibronic energy levels and adopting a relaxation model to account for vibronic cascading down in the donor manifold. We develop a Green's function based generalized formalism and provide an exact solution for the excited state population relaxation and the rate of energy transfer in the presence of vibronic relaxation. We find and verify that the neglect of vibronic relaxations can significantly alter the energy transfer rate and overestimates the distance between D and A.